UV filters, they're definitely a topic of much debate and little consensus. However, Roger at Lensrentals.com has written a great article about why you should never put a cheap UV/Clear filter on a good lens.
From Roger at Lensrentals.com:
Yes, I’m sick of filter articles, too. But I come today not to educate you, but to mock others. Because yes, people continue to try to save a few bucks by putting a cheap filter in front of their $1,000 lens. And also because they buy what they think are good filters off of Fleabay or some used place and these filters aren’t what they think. This can particularly happen when you purchase a brand that makes different filters of differing quality.
How bad can it be, you ask? Well, today we’ll show you. Because someone had a 70-200mm f/2.8 lens that had been nice and sharp and then returned it because it suddenly got soft. They were kind enough to return it with their protective filter in place.
So the first thing we did, as we always do, was put the lens on OLAF, which is simply an array of collimated 5-micron pinholes. A good lens should show and an array of small dots or circles. But this lens showed an array of glaring star flare thingies. Read the full article